The proposed model IMTPP (Intermittently-observed Marked Temporal Point Processes) models the generative distribution of observed events (\(e_k\) ) and missing events (\(\epsilon _r\) ) using MTPP denoted as \(p(\bullet )\)  and \(q(\bullet )\)  respectively. For generating future observed events, we follow a standard sampling procedure [1]}, however, the generation process of missing events is conditioned on the history as well as the next observed event. Specifically, we sample missing events between two observed events, till we reach the future observed event i.e. the MTPP are – \(p(e_k)\)  and \(q(\epsilon _r|e_{k+1})\)  respectively. We learn the parameter by maximizing a variational lower bound or evidence lower bound (ELBO) of the log-likelihood.
\(\mathbb {E}_q \sum _{k=0}^{K-1}\log p(e_{k+1}) - \sum _{k=0}^{K-1} KL \bigg [ q(\epsilon _r | e_{k+1}) || p_r(\epsilon _r))\bigg ],\) 
